Amnon Neeman, The relation between Grothendieck duality and Hochschild homology is an interesting overview article by Amnon. It can be seen as a summary and application of another preprint of his, An improvement on the base-change theorem and the functor $f^!$. It's worth nothing that he simultaneously updated this preprint, which now handles Grothendieck duality for algebraic stacks in the setting of the unbounded derived category (leading to an increase from 76 pages to a whopping 158 pages, which I guess is one way of addressing a reviewer's remark regarding the situation for algebraic stacks).
My favourite group is the semester project that all students in Raf Bocklandt's group theory course have to do. Raf explained me how they choose a group (or rather, a Cayley table) from this list in the first lecture, and that they have to apply each concept they learn throughout the semester to their favourite group. They can interactively check whether their answers are correct (their inputs are fed to GAP). What an awesome idea!